U.S. citizens living outside of the U.S. are only permitted to register and vote in the state and county where they last established residence (domicile) in the U.S. before moving outside of the country. This is your "voting residence address," and it is this address that defines your state and jurisdiction for voting. You cannot use a P.O. Box as your last U.S. address.
When you register to vote and/or request an absentee ballot using the Voter Registration/Absentee Ballot Request form, your local election official in the U.S. will send your ballot and voting materials to your overseas address, not your former U.S. address.
Even if you never voted from your last U.S. address when you lived there, that is the address that you must use.
You don't need to have any current ties with your previous address or state. There is absolutely no requirement for overseas voters to continue to maintain a residence or to own property in the U.S. in order to vote.
Regardless of the length of time you have lived overseas or whether you continue to own property in the U.S., under federal law you continue to maintain the right to vote for federal offices (President, Vice President, U.S. Senator, and U.S. Representative). That federal law is called The Uniformed and Overseas Citizens Absentee Voting Act (UOCAVA). However, to be eligible to vote for state and local offices (such as Governor, State Legislator, County Clerk, Mayor, etc.), you must typically maintain residence/domicile in your last state of residence, even when living overseas. For more details, you will need to check the laws of your state, which you can do so by going to the State Voting Requirements page. Select your state, and on the following page select "Overseas & Military Voters" and “Eligibility Requirements.”